Most of the theory of population genetics is based upon simplifying assumptions, but has, nevertheless, led to some insights concerning population dynamics. Recently, there has been an increasing tendency to use theory in analyzing data from real populations. This has made it important to incorporate more realism, wherever this is possible. For example, it is usually assumed that generations are discrete. We have already done some research on consequences of selection in infinite populations and on stochastic theory for finite populations when there are overlapping generations. These investigations will be pursued further. In addition, the nature and consequences of random mating in such populations will be explored. Simplifying assumptions that are usually made in quantitative genetic theory are that there is no assortative mating and that genetic and environmental effects are additive. Consequences of the violation of these assumptions are under study. Further research will be done on a theory of quantitative genetics which integrates multifactorial genetic determination with occurrence of genetically caused variability in viability. An attempt will also be made to further develop theory of repeated truncation selection that takes account of the changes that occur, due to selection, in the statistical parameters that describe the immediate gain from selection.